Question

given polynomials p(x), q(x), and r(x), p(x)+(q(x)+r(x))=(p(x)+q(x))+r(x). to verify the associative property of addition, begin by finding the sum of the polynomials: (3x + 4)+((5x^2 - 1)+(2x + 6)). which equivalent expression would you set up to verify the associative property of addition for (3x + 4)+((5x^2 - 1)+(2x + 6))? (3x + 4)+(5x^2 - 1); (5x^2 - 1)+((3x + 4)+(2x + 6)); ((3x + 4)+(5x^2 - 1))+(2x + 6); (3x + 4)+(5x^2 - 1)+(2x + 6)

Explanation:

Step1: Recall associative property of addition

The associative property of addition for polynomials states that $(a + b)+c=a+(b + c)$. Here $a = 3x + 4$, $b=5x^{2}-1$ and $c = 2x+6$.

Step2: Identify the equivalent expression

The expression to verify the associative property for $(3x + 4)+((5x^{2}-1)+(2x + 6))$ should be $((3x + 4)+(5x^{2}-1))+(2x + 6)$.

Answer:

C. $((3x + 4)+(5x^{2}-1))+(2x + 6)$